All of this changed around 1985 with the advent of

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Unformatted text preview: ply both signed and unsigned integers. To see this, let Ü ¾Ì Û ´Üµ and Ý ¾Ì Û ´Ý µ be the two’s complement values denoted by these bit patterns, and let ܼ ¾Í Û ´Üµ and Ý ¼ ¾Í Û ´Ý µ be the unsigned values. From Equation 2.3, we have ¼ Ü · ÜÛ ½¾Û , and ݼ Ý · ÝÛ ½¾Û . Computing the product of these values modulo ¾Û gives: Ü ´ ܼ ¡ ݼ µ ÑÓ ¾ Û Ü · Ü ½¾ µ ¡ ´Ý · Ý ½¾ Ü ¡ Ý · ´Ü ½ Ý · Ý ½Üµ¾ ´Ü ¡ Ý µ ÑÓ ¾ ´ Û Û Û Û Û Û Û ÑÓ Û ¾ Û (2.16) ¾Û ÑÓ ¾ Û Û · Ü ½Ý ½ ¾ Û (2.17) (2.18) Thus, the low-order Û bits of Ü ¡ Ý and ܼ ¡ Ý ¼ are identical. 2.3. INTEGER ARITHMETIC Mode Unsigned Two’s Comp. Unsigned Two’s Comp. Unsigned Two’s Comp. 63 Ü Ý ½¼½ ¿ ¿ ¼½½ ¼½½ ½½½ ½ ½½½ ¼½½ ¼½½ ½¼½ ½¼¼ ½¼¼ ¼½½ ¼½½ Ü¡Ý Truncated Ü ¡ Ý ¿ ¾ ½ ¼¼½½½½ ½½¼½½½ ¼½½½¼¼ ¼¼¼½¼¼ ¼¼½¼¼½ ¼¼½¼¼½ ½½½ ½ ½½½ ½¼¼ ½¼¼ ¼¼½ ¼¼½ ¿ ¿ ¿ ¿ ½ ½ Figure 2.21: 3-Bit Unsigned and Two’s Complement Multiplication...
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